Question 1192653: In 2013, Gallup conducted a poll and found a 95% confidence interval of 52% < p < 60%, where p is the proportion of all Americans who believe it is the government’s responsibility to fully fund health care. Which of the following statements about this interval estimate are true (check all answers that apply)?
A) There is a 95% chance that the confidence interval 52% < p < 60% contains the true value of p, the proportion of all Americans who believe it is the government’s responsibility to fully fund health care.
B) The confidence interval estimate 52% < p < 60% was constructed using a procedure that 95% of the time will result in an interval estimate that contains the true value of p, the proportion of all Americans who believe it is the government’s responsibility to fully fund health care.
C) Ninety-five percent of all possible values of p, the proportion of all Americans who believe it is the government’s responsibility to fully fund health care, lie within the interval 52% < p < 60%.
D) There is a 95% chance that the true value of p, the proportion of all Americans who believe it is the government’s responsibility to fully fund health care, will not lie outside the interval 52% < p < 60%.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! B is the best choice.
A needs the word confidence. The true value is either in the interval or it is not. There is no other possibility.
C there is only one value of p, so possible values cannot be the case.
D again, the word confidence has to be used.
We don't know the true value of p. We are 95% confident that the interval we construct will contain that value. If we constructed 100 such intervals, 95 of them would be expected to contain the true value. We just don't know which 95.
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